Whether or not this is actually the entire literal truth is something I am still skeptical about, but there it is...It may well be true.
Bear in mind that up to that point--of the Flores Sea bombing---the HOUSTON had done nothing but escort convoys for the most part. The loss of her 3rd turret & almost fifty men did not hinder her operational ability, really. Her powerplant & hull were fine. Her most serious injury was to her fwd MK19 5" director (Sky Forward)...it was knocked out of action during the engagement by near misses.
At Tjilatjap, as she began undergoing such repairs as could be completed there, ADM Hart (& other Asiatic Fleet officers) visited the damaged cruiser. While they were in the stateroom of CAPT Rooks talking, they got word that a pair of senior CA-30 gunners had actually repaired the fwd director, and it was OK.
At that point I feel that her fate was sealed because her value as an escort was still intact.
They were also able at that time to load many hundred 5" shells for their secondary battery at Tjilatjap--along with a bunch of 3" projectiles by mistake--that had been left behind by BOISE a few days before when she left the theatre. So, they had plenty of 5" ammo (as well as 8") at that point.
I suppose CAPT Rooks wanted to be a 'team player' & did not wish to exit too quickly. Especially with MARBLY (Old Knucklehead) having to leave then. However, I strongly suspect that Hart probably implied (perhaps in a subtle way, perhaps not) that he would not necessarily like CA-30 to leave at that point if at all possible. ABDA's political nature may have factored in, too.
The issue of bringing in PHOENIX might also have been under consideration, but that's another very difficult & complicated story in itself, and far too much of a digression here/now.
However, we were quite short on cruisers in the Pacific at that stage, and that seems to have been another reason CA-30 was needed in the NEI.